MathDB

N2

Part of 2018 Balkan MO Shortlist

Problems(1)

Function with factorial

Source: Shortlist BMO 2018, N2; Albania TST problem 1; Macedonia TST problem 4

5/2/2019
Find all functions f:N→Nf:\mathbb{N}\rightarrow\mathbb{N} such that n!+f(m)!∣f(n)!+f(m!)n!+f(m)!|f(n)!+f(m!) for all m,n∈Nm,n\in\mathbb{N} Proposed by Valmir Krasniqi and Dorlir Ahmeti, Albania
functionfactorialnumber theory